{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:NLXKWXH4PZU4L4SPCNLIC6GEIR","short_pith_number":"pith:NLXKWXH4","canonical_record":{"source":{"id":"1302.0481","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2013-02-03T12:03:18Z","cross_cats_sorted":[],"title_canon_sha256":"350e92e6760e804a815145edea778bbf292d5a2a9205603440e258ea5f3bd71b","abstract_canon_sha256":"0c2a2ec63deacdb03d09b47217b2bf37765f5e6d1751245a932ec8ed04a825e5"},"schema_version":"1.0"},"canonical_sha256":"6aeeab5cfc7e69c5f24f13568178c444491dc08f9fdb8613441dbcd797f3de43","source":{"kind":"arxiv","id":"1302.0481","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.0481","created_at":"2026-05-18T03:32:44Z"},{"alias_kind":"arxiv_version","alias_value":"1302.0481v1","created_at":"2026-05-18T03:32:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.0481","created_at":"2026-05-18T03:32:44Z"},{"alias_kind":"pith_short_12","alias_value":"NLXKWXH4PZU4","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"NLXKWXH4PZU4L4SP","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"NLXKWXH4","created_at":"2026-05-18T12:27:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:NLXKWXH4PZU4L4SPCNLIC6GEIR","target":"record","payload":{"canonical_record":{"source":{"id":"1302.0481","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2013-02-03T12:03:18Z","cross_cats_sorted":[],"title_canon_sha256":"350e92e6760e804a815145edea778bbf292d5a2a9205603440e258ea5f3bd71b","abstract_canon_sha256":"0c2a2ec63deacdb03d09b47217b2bf37765f5e6d1751245a932ec8ed04a825e5"},"schema_version":"1.0"},"canonical_sha256":"6aeeab5cfc7e69c5f24f13568178c444491dc08f9fdb8613441dbcd797f3de43","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:32:44.314267Z","signature_b64":"IKQfRJH5Gcj/HqSIgk/Z7jUOyz1ErucH0QUO+OOhYkLzFh922gcpSQnjrkD86+RhdLFgWTob1x1GIS14OialCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6aeeab5cfc7e69c5f24f13568178c444491dc08f9fdb8613441dbcd797f3de43","last_reissued_at":"2026-05-18T03:32:44.313746Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:32:44.313746Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1302.0481","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:32:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hL1KYd8gSg/JCj36Q39SbmJCjH/+MBu+tefPFOtEaSAtDr9Itz2NPxXytOZa3yG0yeeC5Hs14xItYAVeMyj0AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T16:58:56.819817Z"},"content_sha256":"c7dbf23092b985b492e0fc2da7bb3e6ebc5e4bf29a2231e64314c8d800874aab","schema_version":"1.0","event_id":"sha256:c7dbf23092b985b492e0fc2da7bb3e6ebc5e4bf29a2231e64314c8d800874aab"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:NLXKWXH4PZU4L4SPCNLIC6GEIR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Long-Range and Many-Body Effects in Coagulation Processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Anton A. Winkler, Erwin Frey","submitted_at":"2013-02-03T12:03:18Z","abstract_excerpt":"We study the problem of diffusing particles which coalesce upon contact. With the aid of a non-perturbative renormalization group, we first analyze the dynamics emerging below the critical dimension two, where strong fluctuations imply anomalously slow decay. Above two dimensions, the long-time, low-density behavior is known to conform with the law of mass action. For this case, we establish an exact mapping between the physics at the microscopic scale (lattice structure, particle shape and size) and the macroscopic decay rate in the law of mass action. In addition, we identify a term violatin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.0481","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:32:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jVqOAylvYojAcMqU1bX80n76oEFIyZYzcxTfxFmeiXrDLp77IRcT89/glM5lolc1P6ePoNfEMDiq0ynOuh2GDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T16:58:56.820484Z"},"content_sha256":"de3007f3a976146988509472d1ec67b3a3e225d44ffb20beb89990ee4f69cb33","schema_version":"1.0","event_id":"sha256:de3007f3a976146988509472d1ec67b3a3e225d44ffb20beb89990ee4f69cb33"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NLXKWXH4PZU4L4SPCNLIC6GEIR/bundle.json","state_url":"https://pith.science/pith/NLXKWXH4PZU4L4SPCNLIC6GEIR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NLXKWXH4PZU4L4SPCNLIC6GEIR/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-06T16:58:56Z","links":{"resolver":"https://pith.science/pith/NLXKWXH4PZU4L4SPCNLIC6GEIR","bundle":"https://pith.science/pith/NLXKWXH4PZU4L4SPCNLIC6GEIR/bundle.json","state":"https://pith.science/pith/NLXKWXH4PZU4L4SPCNLIC6GEIR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NLXKWXH4PZU4L4SPCNLIC6GEIR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:NLXKWXH4PZU4L4SPCNLIC6GEIR","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"0c2a2ec63deacdb03d09b47217b2bf37765f5e6d1751245a932ec8ed04a825e5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2013-02-03T12:03:18Z","title_canon_sha256":"350e92e6760e804a815145edea778bbf292d5a2a9205603440e258ea5f3bd71b"},"schema_version":"1.0","source":{"id":"1302.0481","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.0481","created_at":"2026-05-18T03:32:44Z"},{"alias_kind":"arxiv_version","alias_value":"1302.0481v1","created_at":"2026-05-18T03:32:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.0481","created_at":"2026-05-18T03:32:44Z"},{"alias_kind":"pith_short_12","alias_value":"NLXKWXH4PZU4","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"NLXKWXH4PZU4L4SP","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"NLXKWXH4","created_at":"2026-05-18T12:27:52Z"}],"graph_snapshots":[{"event_id":"sha256:de3007f3a976146988509472d1ec67b3a3e225d44ffb20beb89990ee4f69cb33","target":"graph","created_at":"2026-05-18T03:32:44Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We study the problem of diffusing particles which coalesce upon contact. With the aid of a non-perturbative renormalization group, we first analyze the dynamics emerging below the critical dimension two, where strong fluctuations imply anomalously slow decay. Above two dimensions, the long-time, low-density behavior is known to conform with the law of mass action. For this case, we establish an exact mapping between the physics at the microscopic scale (lattice structure, particle shape and size) and the macroscopic decay rate in the law of mass action. In addition, we identify a term violatin","authors_text":"Anton A. Winkler, Erwin Frey","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2013-02-03T12:03:18Z","title":"Long-Range and Many-Body Effects in Coagulation Processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.0481","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:c7dbf23092b985b492e0fc2da7bb3e6ebc5e4bf29a2231e64314c8d800874aab","target":"record","created_at":"2026-05-18T03:32:44Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"0c2a2ec63deacdb03d09b47217b2bf37765f5e6d1751245a932ec8ed04a825e5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2013-02-03T12:03:18Z","title_canon_sha256":"350e92e6760e804a815145edea778bbf292d5a2a9205603440e258ea5f3bd71b"},"schema_version":"1.0","source":{"id":"1302.0481","kind":"arxiv","version":1}},"canonical_sha256":"6aeeab5cfc7e69c5f24f13568178c444491dc08f9fdb8613441dbcd797f3de43","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6aeeab5cfc7e69c5f24f13568178c444491dc08f9fdb8613441dbcd797f3de43","first_computed_at":"2026-05-18T03:32:44.313746Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:32:44.313746Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IKQfRJH5Gcj/HqSIgk/Z7jUOyz1ErucH0QUO+OOhYkLzFh922gcpSQnjrkD86+RhdLFgWTob1x1GIS14OialCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:32:44.314267Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.0481","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c7dbf23092b985b492e0fc2da7bb3e6ebc5e4bf29a2231e64314c8d800874aab","sha256:de3007f3a976146988509472d1ec67b3a3e225d44ffb20beb89990ee4f69cb33"],"state_sha256":"aa7735ce581c32ada20cb7df53472e4839464ee23aedac24889a12e85f1bdc70"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xG9cpTHXBWwy49TW6ECrF+G0cBTQUjyDFV7GWobK5TXRCyVlJC8q4t4G0Zfi3+7AJZ/lkWp3Zr+GbhXnVhgVCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T16:58:56.824008Z","bundle_sha256":"22f129ab1149a022ced8fbd7c67e78b68f4781e0f08e35fb3c8b24b0d3c3340b"}}